Discrete projection methods for Fredholm–Hammerstein integral equations using Kumar and Sloan technique

Abstract

The proposed work discusses discrete collocation and discrete Galerkin methods for second kind Fredholm–Hammerstein integral equations on half line \([0,\infty )\) using Kumar and Sloan technique. In addition, the finite section approximation method is applied to transform the domain of integration from \([0, \infty )\) to \([0,\alpha ],~ \alpha >0\). In contrast to previous studies in which the optimal order of convergence is achieved for projection methods, we attained superconvergence rates in uniform norm using piecewise polynomial basis function. Moreover, these superconvergence rates are further enhanced by using discrete multi-projection (collocation and Galerkin) methods. In order to support the provided theoretical framework, numerical examples are included as well.